My raspberry pi 3 is getting really hot as soon as it is plugged in. Its temperature is resting at about 65-70 C when it isn't doing anything and I've read that it shouldn't exceed 85 C. The room it is in is only about 23 C and it is sitting on a table not in a case. Is this normal?
That sounds a little high, but mine tend to sit in the high 50s °C when idle. Heatsinks - even small ones - can help quite a bit
If it gets very hot very quickly (a few seconds) that is a symptom of frying the GPIO in an experiment which went wrong.
If you do mean very hot in a few seconds it may indicate a Pi which is about to fail.